Tur\'an type inequalities for Tricomi confluent hypergeometric functions

TL;DR

This paper establishes sharp Turán type inequalities for Tricomi confluent hypergeometric functions, using integral representations, and explores their monotonicity properties, advancing the mathematical understanding of these special functions.

Contribution

It introduces new sharp inequalities and monotonicity results for Tricomi confluent hypergeometric functions, improving upon previous findings.

Findings

Derived sharp two-sided Turán inequalities

Established complete monotonicity of Turán determinants

Enhanced understanding of special function inequalities

Abstract

Some sharp two-sided Tur\'an type inequalities for parabolic cylinder functions and Tricomi confluent hypergeometric functions are deduced. The proofs are based on integral representations for quotients of parabolic cylinder functions and Tricomi confluent hypergeometric functions, which arise in the study of the infinite divisibility of the Fisher-Snedecor F distribution. Moroever, some complete monotonicity results are given concerning Tur\'an determinants of Tricomi confluent hypergeometric functions. These complement and improve some of the results of Ismail and Laforgia [23].